Problem: Simplify to lowest terms. $\dfrac{98}{70}$
Explanation: There are several ways to tackle this problem. What is the greatest common factor (GCD) of 98 and 70? $98 = 2\cdot7\cdot7$ $70 = 2\cdot5\cdot7$ $\mbox{GCD}(98, 70) = 2\cdot7 = 14$ $\dfrac{98}{70} = \dfrac{7 \cdot 14}{ 5\cdot 14}$ $\hphantom{\dfrac{98}{70}} = \dfrac{7}{5} \cdot \dfrac{14}{14}$ $\hphantom{\dfrac{98}{70}} = \dfrac{7}{5} \cdot 1$ $\hphantom{\dfrac{98}{70}} = \dfrac{7}{5}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{98}{70}= \dfrac{2\cdot49}{2\cdot35}= \dfrac{2\cdot 7\cdot7}{2\cdot 7\cdot5}= \dfrac{7}{5}$